3.24.92 \(\int \frac {-1665+570 x-240 x^2+720 x^3-285 x^4+30 x^5+(60-300 x+435 x^2-150 x^3+15 x^4) \log (x)}{4-20 x+29 x^2-10 x^3+x^4} \, dx\)

Optimal. Leaf size=23 \[ 15 \left (2+\frac {5}{\frac {2}{-5+x}+x}+x (x+\log (x))\right ) \]

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Rubi [B]  time = 0.56, antiderivative size = 320, normalized size of antiderivative = 13.91, number of steps used = 31, number of rules used = 14, integrand size = 69, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.203, Rules used = {6688, 12, 6742, 614, 618, 206, 638, 722, 738, 773, 632, 31, 800, 2295} \begin {gather*} \frac {150 x^3}{17}+\frac {720 (4-5 x) x^2}{17 \left (x^2-5 x+2\right )}-\frac {540 x^2}{17}-\frac {240 (4-5 x) x}{17 \left (x^2-5 x+2\right )}+\frac {570 (4-5 x)}{17 \left (x^2-5 x+2\right )}-\frac {1665 (5-2 x)}{17 \left (x^2-5 x+2\right )}+\frac {30 (4-5 x) x^4}{17 \left (x^2-5 x+2\right )}-\frac {285 (4-5 x) x^3}{17 \left (x^2-5 x+2\right )}+\frac {465 x}{17}+15 x \log (x)+\frac {360}{289} \left (289-65 \sqrt {17}\right ) \log \left (-2 x-\sqrt {17}+5\right )-\frac {285}{289} \left (1445-349 \sqrt {17}\right ) \log \left (-2 x-\sqrt {17}+5\right )+\frac {15}{289} \left (20519-4975 \sqrt {17}\right ) \log \left (-2 x-\sqrt {17}+5\right )+\frac {15}{289} \left (20519+4975 \sqrt {17}\right ) \log \left (-2 x+\sqrt {17}+5\right )-\frac {285}{289} \left (1445+349 \sqrt {17}\right ) \log \left (-2 x+\sqrt {17}+5\right )+\frac {360}{289} \left (289+65 \sqrt {17}\right ) \log \left (-2 x+\sqrt {17}+5\right )+\frac {2880 \tanh ^{-1}\left (\frac {5-2 x}{\sqrt {17}}\right )}{17 \sqrt {17}} \end {gather*}

Antiderivative was successfully verified.

[In]

Int[(-1665 + 570*x - 240*x^2 + 720*x^3 - 285*x^4 + 30*x^5 + (60 - 300*x + 435*x^2 - 150*x^3 + 15*x^4)*Log[x])/
(4 - 20*x + 29*x^2 - 10*x^3 + x^4),x]

[Out]

(465*x)/17 - (540*x^2)/17 + (150*x^3)/17 + (570*(4 - 5*x))/(17*(2 - 5*x + x^2)) - (1665*(5 - 2*x))/(17*(2 - 5*
x + x^2)) - (240*(4 - 5*x)*x)/(17*(2 - 5*x + x^2)) + (720*(4 - 5*x)*x^2)/(17*(2 - 5*x + x^2)) - (285*(4 - 5*x)
*x^3)/(17*(2 - 5*x + x^2)) + (30*(4 - 5*x)*x^4)/(17*(2 - 5*x + x^2)) + (2880*ArcTanh[(5 - 2*x)/Sqrt[17]])/(17*
Sqrt[17]) + (15*(20519 - 4975*Sqrt[17])*Log[5 - Sqrt[17] - 2*x])/289 - (285*(1445 - 349*Sqrt[17])*Log[5 - Sqrt
[17] - 2*x])/289 + (360*(289 - 65*Sqrt[17])*Log[5 - Sqrt[17] - 2*x])/289 + (360*(289 + 65*Sqrt[17])*Log[5 + Sq
rt[17] - 2*x])/289 - (285*(1445 + 349*Sqrt[17])*Log[5 + Sqrt[17] - 2*x])/289 + (15*(20519 + 4975*Sqrt[17])*Log
[5 + Sqrt[17] - 2*x])/289 + 15*x*Log[x]

Rule 12

Int[(a_)*(u_), x_Symbol] :> Dist[a, Int[u, x], x] /; FreeQ[a, x] &&  !MatchQ[u, (b_)*(v_) /; FreeQ[b, x]]

Rule 31

Int[((a_) + (b_.)*(x_))^(-1), x_Symbol] :> Simp[Log[RemoveContent[a + b*x, x]]/b, x] /; FreeQ[{a, b}, x]

Rule 206

Int[((a_) + (b_.)*(x_)^2)^(-1), x_Symbol] :> Simp[(1*ArcTanh[(Rt[-b, 2]*x)/Rt[a, 2]])/(Rt[a, 2]*Rt[-b, 2]), x]
/; FreeQ[{a, b}, x] && NegQ[a/b] && (GtQ[a, 0] || LtQ[b, 0])

Rule 614

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((b + 2*c*x)*(a + b*x + c*x^2)^(p + 1))/((p +
1)*(b^2 - 4*a*c)), x] - Dist[(2*c*(2*p + 3))/((p + 1)*(b^2 - 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1), x], x] /;
FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0] && LtQ[p, -1] && NeQ[p, -3/2] && IntegerQ[4*p]

Rule 618

Int[((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(-1), x_Symbol] :> Dist[-2, Subst[Int[1/Simp[b^2 - 4*a*c - x^2, x], x]
, x, b + 2*c*x], x] /; FreeQ[{a, b, c}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 632

Int[((d_.) + (e_.)*(x_))/((a_) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> With[{q = Rt[b^2 - 4*a*c, 2]}, Dist[
(c*d - e*(b/2 - q/2))/q, Int[1/(b/2 - q/2 + c*x), x], x] - Dist[(c*d - e*(b/2 + q/2))/q, Int[1/(b/2 + q/2 + c*
x), x], x]] /; FreeQ[{a, b, c, d, e}, x] && NeQ[2*c*d - b*e, 0] && NeQ[b^2 - 4*a*c, 0] && NiceSqrtQ[b^2 - 4*a*
c]

Rule 638

Int[((d_.) + (e_.)*(x_))*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((b*d - 2*a*e + (2*c*d -
b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] - Dist[((2*p + 3)*(2*c*d - b*e))/((p + 1)*(b^2
- 4*a*c)), Int[(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[2*c*d - b*e, 0] && NeQ[b^
2 - 4*a*c, 0] && LtQ[p, -1] && NeQ[p, -3/2]

Rule 722

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^(m - 1)*(
d*b - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] - Dist[(2*(2*p + 3)*(c*d
^2 - b*d*e + a*e^2))/((p + 1)*(b^2 - 4*a*c)), Int[(d + e*x)^(m - 2)*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ
[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && EqQ[m +
2*p + 2, 0] && LtQ[p, -1]

Rule 738

Int[((d_.) + (e_.)*(x_))^(m_)*((a_.) + (b_.)*(x_) + (c_.)*(x_)^2)^(p_), x_Symbol] :> Simp[((d + e*x)^(m - 1)*(
d*b - 2*a*e + (2*c*d - b*e)*x)*(a + b*x + c*x^2)^(p + 1))/((p + 1)*(b^2 - 4*a*c)), x] + Dist[1/((p + 1)*(b^2 -
4*a*c)), Int[(d + e*x)^(m - 2)*Simp[e*(2*a*e*(m - 1) + b*d*(2*p - m + 4)) - 2*c*d^2*(2*p + 3) + e*(b*e - 2*d*
c)*(m + 2*p + 2)*x, x]*(a + b*x + c*x^2)^(p + 1), x], x] /; FreeQ[{a, b, c, d, e}, x] && NeQ[b^2 - 4*a*c, 0] &
& NeQ[c*d^2 - b*d*e + a*e^2, 0] && NeQ[2*c*d - b*e, 0] && LtQ[p, -1] && GtQ[m, 1] && IntQuadraticQ[a, b, c, d,
e, m, p, x]

Rule 773

Int[(((d_.) + (e_.)*(x_))*((f_) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Simp[(e*g*x)/
c, x] + Dist[1/c, Int[(c*d*f - a*e*g + (c*e*f + c*d*g - b*e*g)*x)/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c,
d, e, f, g}, x] && NeQ[b^2 - 4*a*c, 0]

Rule 800

Int[(((d_.) + (e_.)*(x_))^(m_)*((f_.) + (g_.)*(x_)))/((a_.) + (b_.)*(x_) + (c_.)*(x_)^2), x_Symbol] :> Int[Exp
andIntegrand[((d + e*x)^m*(f + g*x))/(a + b*x + c*x^2), x], x] /; FreeQ[{a, b, c, d, e, f, g}, x] && NeQ[b^2 -
4*a*c, 0] && NeQ[c*d^2 - b*d*e + a*e^2, 0] && IntegerQ[m]

Rule 2295

Int[Log[(c_.)*(x_)^(n_.)], x_Symbol] :> Simp[x*Log[c*x^n], x] - Simp[n*x, x] /; FreeQ[{c, n}, x]

Rule 6688

Int[u_, x_Symbol] :> With[{v = SimplifyIntegrand[u, x]}, Int[v, x] /; SimplerIntegrandQ[v, u, x]]

Rule 6742

Int[u_, x_Symbol] :> With[{v = ExpandIntegrand[u, x]}, Int[v, x] /; SumQ[v]]

Rubi steps

\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {15 \left (-111+38 x-16 x^2+48 x^3-19 x^4+2 x^5+\left (2-5 x+x^2\right )^2 \log (x)\right )}{\left (2-5 x+x^2\right )^2} \, dx\\ &=15 \int \frac {-111+38 x-16 x^2+48 x^3-19 x^4+2 x^5+\left (2-5 x+x^2\right )^2 \log (x)}{\left (2-5 x+x^2\right )^2} \, dx\\ &=15 \int \left (-\frac {111}{\left (2-5 x+x^2\right )^2}+\frac {38 x}{\left (2-5 x+x^2\right )^2}-\frac {16 x^2}{\left (2-5 x+x^2\right )^2}+\frac {48 x^3}{\left (2-5 x+x^2\right )^2}-\frac {19 x^4}{\left (2-5 x+x^2\right )^2}+\frac {2 x^5}{\left (2-5 x+x^2\right )^2}+\log (x)\right ) \, dx\\ &=15 \int \log (x) \, dx+30 \int \frac {x^5}{\left (2-5 x+x^2\right )^2} \, dx-240 \int \frac {x^2}{\left (2-5 x+x^2\right )^2} \, dx-285 \int \frac {x^4}{\left (2-5 x+x^2\right )^2} \, dx+570 \int \frac {x}{\left (2-5 x+x^2\right )^2} \, dx+720 \int \frac {x^3}{\left (2-5 x+x^2\right )^2} \, dx-1665 \int \frac {1}{\left (2-5 x+x^2\right )^2} \, dx\\ &=-15 x+\frac {570 (4-5 x)}{17 \left (2-5 x+x^2\right )}-\frac {1665 (5-2 x)}{17 \left (2-5 x+x^2\right )}-\frac {240 (4-5 x) x}{17 \left (2-5 x+x^2\right )}+\frac {720 (4-5 x) x^2}{17 \left (2-5 x+x^2\right )}-\frac {285 (4-5 x) x^3}{17 \left (2-5 x+x^2\right )}+\frac {30 (4-5 x) x^4}{17 \left (2-5 x+x^2\right )}+15 x \log (x)-\frac {30}{17} \int \frac {(16-15 x) x^3}{2-5 x+x^2} \, dx+\frac {285}{17} \int \frac {(12-10 x) x^2}{2-5 x+x^2} \, dx-\frac {720}{17} \int \frac {(8-5 x) x}{2-5 x+x^2} \, dx+\frac {960}{17} \int \frac {1}{2-5 x+x^2} \, dx-\frac {2850}{17} \int \frac {1}{2-5 x+x^2} \, dx+\frac {3330}{17} \int \frac {1}{2-5 x+x^2} \, dx\\ &=\frac {3345 x}{17}+\frac {570 (4-5 x)}{17 \left (2-5 x+x^2\right )}-\frac {1665 (5-2 x)}{17 \left (2-5 x+x^2\right )}-\frac {240 (4-5 x) x}{17 \left (2-5 x+x^2\right )}+\frac {720 (4-5 x) x^2}{17 \left (2-5 x+x^2\right )}-\frac {285 (4-5 x) x^3}{17 \left (2-5 x+x^2\right )}+\frac {30 (4-5 x) x^4}{17 \left (2-5 x+x^2\right )}+15 x \log (x)-\frac {30}{17} \int \left (-265-59 x-15 x^2+\frac {530-1207 x}{2-5 x+x^2}\right ) \, dx+\frac {285}{17} \int \left (-38-10 x+\frac {2 (38-85 x)}{2-5 x+x^2}\right ) \, dx-\frac {720}{17} \int \frac {10-17 x}{2-5 x+x^2} \, dx-\frac {1920}{17} \operatorname {Subst}\left (\int \frac {1}{17-x^2} \, dx,x,-5+2 x\right )+\frac {5700}{17} \operatorname {Subst}\left (\int \frac {1}{17-x^2} \, dx,x,-5+2 x\right )-\frac {6660}{17} \operatorname {Subst}\left (\int \frac {1}{17-x^2} \, dx,x,-5+2 x\right )\\ &=\frac {465 x}{17}-\frac {540 x^2}{17}+\frac {150 x^3}{17}+\frac {570 (4-5 x)}{17 \left (2-5 x+x^2\right )}-\frac {1665 (5-2 x)}{17 \left (2-5 x+x^2\right )}-\frac {240 (4-5 x) x}{17 \left (2-5 x+x^2\right )}+\frac {720 (4-5 x) x^2}{17 \left (2-5 x+x^2\right )}-\frac {285 (4-5 x) x^3}{17 \left (2-5 x+x^2\right )}+\frac {30 (4-5 x) x^4}{17 \left (2-5 x+x^2\right )}+\frac {2880 \tanh ^{-1}\left (\frac {5-2 x}{\sqrt {17}}\right )}{17 \sqrt {17}}+15 x \log (x)-\frac {30}{17} \int \frac {530-1207 x}{2-5 x+x^2} \, dx+\frac {570}{17} \int \frac {38-85 x}{2-5 x+x^2} \, dx+\frac {1}{289} \left (360 \left (289-65 \sqrt {17}\right )\right ) \int \frac {1}{-\frac {5}{2}+\frac {\sqrt {17}}{2}+x} \, dx+\frac {1}{289} \left (360 \left (289+65 \sqrt {17}\right )\right ) \int \frac {1}{-\frac {5}{2}-\frac {\sqrt {17}}{2}+x} \, dx\\ &=\frac {465 x}{17}-\frac {540 x^2}{17}+\frac {150 x^3}{17}+\frac {570 (4-5 x)}{17 \left (2-5 x+x^2\right )}-\frac {1665 (5-2 x)}{17 \left (2-5 x+x^2\right )}-\frac {240 (4-5 x) x}{17 \left (2-5 x+x^2\right )}+\frac {720 (4-5 x) x^2}{17 \left (2-5 x+x^2\right )}-\frac {285 (4-5 x) x^3}{17 \left (2-5 x+x^2\right )}+\frac {30 (4-5 x) x^4}{17 \left (2-5 x+x^2\right )}+\frac {2880 \tanh ^{-1}\left (\frac {5-2 x}{\sqrt {17}}\right )}{17 \sqrt {17}}+\frac {360}{289} \left (289-65 \sqrt {17}\right ) \log \left (5-\sqrt {17}-2 x\right )+\frac {360}{289} \left (289+65 \sqrt {17}\right ) \log \left (5+\sqrt {17}-2 x\right )+15 x \log (x)+\frac {1}{289} \left (15 \left (20519-4975 \sqrt {17}\right )\right ) \int \frac {1}{-\frac {5}{2}+\frac {\sqrt {17}}{2}+x} \, dx-\frac {1}{289} \left (285 \left (1445-349 \sqrt {17}\right )\right ) \int \frac {1}{-\frac {5}{2}+\frac {\sqrt {17}}{2}+x} \, dx-\frac {1}{289} \left (285 \left (1445+349 \sqrt {17}\right )\right ) \int \frac {1}{-\frac {5}{2}-\frac {\sqrt {17}}{2}+x} \, dx+\frac {1}{289} \left (15 \left (20519+4975 \sqrt {17}\right )\right ) \int \frac {1}{-\frac {5}{2}-\frac {\sqrt {17}}{2}+x} \, dx\\ &=\frac {465 x}{17}-\frac {540 x^2}{17}+\frac {150 x^3}{17}+\frac {570 (4-5 x)}{17 \left (2-5 x+x^2\right )}-\frac {1665 (5-2 x)}{17 \left (2-5 x+x^2\right )}-\frac {240 (4-5 x) x}{17 \left (2-5 x+x^2\right )}+\frac {720 (4-5 x) x^2}{17 \left (2-5 x+x^2\right )}-\frac {285 (4-5 x) x^3}{17 \left (2-5 x+x^2\right )}+\frac {30 (4-5 x) x^4}{17 \left (2-5 x+x^2\right )}+\frac {2880 \tanh ^{-1}\left (\frac {5-2 x}{\sqrt {17}}\right )}{17 \sqrt {17}}+\frac {15}{289} \left (20519-4975 \sqrt {17}\right ) \log \left (5-\sqrt {17}-2 x\right )-\frac {285}{289} \left (1445-349 \sqrt {17}\right ) \log \left (5-\sqrt {17}-2 x\right )+\frac {360}{289} \left (289-65 \sqrt {17}\right ) \log \left (5-\sqrt {17}-2 x\right )+\frac {360}{289} \left (289+65 \sqrt {17}\right ) \log \left (5+\sqrt {17}-2 x\right )-\frac {285}{289} \left (1445+349 \sqrt {17}\right ) \log \left (5+\sqrt {17}-2 x\right )+\frac {15}{289} \left (20519+4975 \sqrt {17}\right ) \log \left (5+\sqrt {17}-2 x\right )+15 x \log (x)\\ \end {aligned} \end {gather*}

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Mathematica [A]  time = 0.11, size = 25, normalized size = 1.09 \begin {gather*} 15 \left (x^2+\frac {5 (-5+x)}{2-5 x+x^2}+x \log (x)\right ) \end {gather*}

Antiderivative was successfully verified.

[In]

Integrate[(-1665 + 570*x - 240*x^2 + 720*x^3 - 285*x^4 + 30*x^5 + (60 - 300*x + 435*x^2 - 150*x^3 + 15*x^4)*Lo
g[x])/(4 - 20*x + 29*x^2 - 10*x^3 + x^4),x]

[Out]

15*(x^2 + (5*(-5 + x))/(2 - 5*x + x^2) + x*Log[x])

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fricas [B]  time = 0.91, size = 45, normalized size = 1.96 \begin {gather*} \frac {15 \, {\left (x^{4} - 5 \, x^{3} + 2 \, x^{2} + {\left (x^{3} - 5 \, x^{2} + 2 \, x\right )} \log \relax (x) + 5 \, x - 25\right )}}{x^{2} - 5 \, x + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^4-150*x^3+435*x^2-300*x+60)*log(x)+30*x^5-285*x^4+720*x^3-240*x^2+570*x-1665)/(x^4-10*x^3+29*
x^2-20*x+4),x, algorithm="fricas")

[Out]

15*(x^4 - 5*x^3 + 2*x^2 + (x^3 - 5*x^2 + 2*x)*log(x) + 5*x - 25)/(x^2 - 5*x + 2)

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giac [A]  time = 0.18, size = 26, normalized size = 1.13 \begin {gather*} 15 \, x^{2} + 15 \, x \log \relax (x) + \frac {75 \, {\left (x - 5\right )}}{x^{2} - 5 \, x + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^4-150*x^3+435*x^2-300*x+60)*log(x)+30*x^5-285*x^4+720*x^3-240*x^2+570*x-1665)/(x^4-10*x^3+29*
x^2-20*x+4),x, algorithm="giac")

[Out]

15*x^2 + 15*x*log(x) + 75*(x - 5)/(x^2 - 5*x + 2)

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maple [A]  time = 0.04, size = 29, normalized size = 1.26

method	result	size
default	\(15 x^{2}-\frac {75 \left (5-x \right )}{x^{2}-5 x +2}+15 x \ln \relax (x )\)	\(29\)
risch	\(15 x \ln \relax (x )+\frac {15 x^{4}-75 x^{3}+30 x^{2}+75 x -375}{x^{2}-5 x +2}\)	\(37\)
norman	\(\frac {225 x -75 x^{3}+15 x^{4}+30 x \ln \relax (x )-75 x^{2} \ln \relax (x )+15 x^{3} \ln \relax (x )-435}{x^{2}-5 x +2}\)	\(46\)

Verification of antiderivative is not currently implemented for this CAS.

[In]

int(((15*x^4-150*x^3+435*x^2-300*x+60)*ln(x)+30*x^5-285*x^4+720*x^3-240*x^2+570*x-1665)/(x^4-10*x^3+29*x^2-20*
x+4),x,method=_RETURNVERBOSE)

[Out]

15*x^2-75*(5-x)/(x^2-5*x+2)+15*x*ln(x)

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maxima [B]  time = 0.60, size = 113, normalized size = 4.91 \begin {gather*} 15 \, x^{2} + 15 \, x \log \relax (x) - \frac {30 \, {\left (1975 \, x - 866\right )}}{17 \, {\left (x^{2} - 5 \, x + 2\right )}} + \frac {285 \, {\left (433 \, x - 190\right )}}{17 \, {\left (x^{2} - 5 \, x + 2\right )}} - \frac {720 \, {\left (95 \, x - 42\right )}}{17 \, {\left (x^{2} - 5 \, x + 2\right )}} + \frac {240 \, {\left (21 \, x - 10\right )}}{17 \, {\left (x^{2} - 5 \, x + 2\right )}} - \frac {570 \, {\left (5 \, x - 4\right )}}{17 \, {\left (x^{2} - 5 \, x + 2\right )}} + \frac {1665 \, {\left (2 \, x - 5\right )}}{17 \, {\left (x^{2} - 5 \, x + 2\right )}} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x^4-150*x^3+435*x^2-300*x+60)*log(x)+30*x^5-285*x^4+720*x^3-240*x^2+570*x-1665)/(x^4-10*x^3+29*
x^2-20*x+4),x, algorithm="maxima")

[Out]

15*x^2 + 15*x*log(x) - 30/17*(1975*x - 866)/(x^2 - 5*x + 2) + 285/17*(433*x - 190)/(x^2 - 5*x + 2) - 720/17*(9
5*x - 42)/(x^2 - 5*x + 2) + 240/17*(21*x - 10)/(x^2 - 5*x + 2) - 570/17*(5*x - 4)/(x^2 - 5*x + 2) + 1665/17*(2
*x - 5)/(x^2 - 5*x + 2)

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mupad [B]  time = 1.46, size = 27, normalized size = 1.17 \begin {gather*} \frac {75\,x-375}{x^2-5\,x+2}+15\,x\,\ln \relax (x)+15\,x^2 \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

int((570*x + log(x)*(435*x^2 - 300*x - 150*x^3 + 15*x^4 + 60) - 240*x^2 + 720*x^3 - 285*x^4 + 30*x^5 - 1665)/(
29*x^2 - 20*x - 10*x^3 + x^4 + 4),x)

[Out]

(75*x - 375)/(x^2 - 5*x + 2) + 15*x*log(x) + 15*x^2

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sympy [A]  time = 0.16, size = 24, normalized size = 1.04 \begin {gather*} 15 x^{2} + 15 x \log {\relax (x )} + \frac {75 x - 375}{x^{2} - 5 x + 2} \end {gather*}

Verification of antiderivative is not currently implemented for this CAS.

[In]

integrate(((15*x**4-150*x**3+435*x**2-300*x+60)*ln(x)+30*x**5-285*x**4+720*x**3-240*x**2+570*x-1665)/(x**4-10*
x**3+29*x**2-20*x+4),x)

[Out]

15*x**2 + 15*x*log(x) + (75*x - 375)/(x**2 - 5*x + 2)

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